New Zealand First leader and acting Prime Minister Winston Peters said it's a "happy day".

"On behalf of the coalition government we wish her and Clarke all the very best."

In a statement, Deputy Labour leader Kelvin Davis said this is an "exciting and unforgettable time" for the couple.

"I am sure that all New Zealanders join with me in celebrating the birth of their first child.

"It is also momentous for our country. As the first Prime Minister in New Zealand to have a baby while in office and the first elected leader ever to take maternity leave, Jacinda is an inspiration to all of us."

Minster of Justice Andrew Little shared a short video wearing a party hat, blowing a party popper, and waving a 'congratulations' sign.

Minister of Finance Grant Robertson also took to Twitter to congratulate the couple.

"Oh my heart. So happy for and proud of my friend. You two will be the very best parents. Congrats!!"

Opposition leader Simon Bridges put his usual rivalry with Ms Ardern aside as he tweeted his well wishes.

"Congratulations on the birth of your baby girl, Natalie and I wish you every happiness."

The Green Party released a statement extending their love and congratulations.

"It is with great joy that I, on behalf of the Green Party, congratulate the Prime Minister and Clarke Gayford on the wonderful news that their baby girl has been born," said Green Party Co-leader Marama Davidson.

"As a mum, my heart is bursting with pride and love for the Prime Minister and her whānau and wish them the very best for their future.

"The Prime Minister having a baby while in office is a symbolically significant moment for our country, women in particular, and sends an important message that caring for children is one of the most important jobs in the world," said Ms Davidson.

The Green Party caucus is sending a card to the new parents and giving a koha on their behalf to wahakura weavers. The Prime Minister was given a wahakura for her baby at Waitangi this year by Māori public health agency Hāpai Te Hauora.

Former Prime Minister Helen Clark says this is what 21st century New Zealand looks like.

"Congratulations to Jacinda Ardern & Clarke Gayford on the birth of their daughter today. What a proud day for Jacinda & Clarke & for us all. New life, new hope. Parenting arrangements are #genderequality in action. This is 21st C NZ," she wrote.

ACT leader David Seymour also shared his well wishes.

"Congratulations to Jacinda and Clarke on their new arrival wishing them all the very best."

Jacinda Ardern shared the news on Instagram just after 6pm on Thursday.

"Welcome to our village wee one. Feeling very lucky to have a healthy baby girl that arrived at 4:45pm weighing 3.31kg.

"Thank you so much for your best wishes and your kindness. We're all doing really well thanks to the wonderful team at Auckland City Hospital."